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The use of numerical methods to solve systems of partial differential equations for chemical kinetics is introduced using a Mathematica notebook. The principles of numerical integration are briefly presented. The Runge–Kutta algorithm is used to explore two simple mechanisms as well as an auto-catalyzed system (Lotka–Volterra) which exhibits exotic kinetic behaviors. The exercise can be used in the introductory physical chemistry course as a capstone exercise for chemical kinetics, or in the lecture to introduce numerical methods and exotic kinetic behaviors such as oscillatory reactions and chaotic behavior. An exercise for mastery based on the Gray–Scott mechanism for glycolysis is included. 
Figure 1. Lotka–Voltera concentration variation for [X] (♦) and [Y] (*), as a function of time.
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